f2 = c/(12 pi^2)

Status: proved — a complete structured proof.

Area: Theorem A: exact recovery error of the free fermion · Card type: constant · Knowledge-base id: const-f2

Statement

Second-order coefficient of the recovery error per chirality: f2 = c/(12 pi^2) = 0.0084434 c; numerically 0.008444(1) for c = 1. For the ordinary Petz map with both chiralities (massless Dirac fermion, card two-chirality-law; for a general 2D CFT this rests on the unproved chiral factorisation of card two-chirality-law-general-cft) the coefficient is 8 f2 in z^2; for the compression 2 f2 z^2; in Vardhan-Wei-Zou variables at lambda = 0 this is 0.0169 c eta^2 (compression) against 0.0676 c eta^2 = 8 f2 eta^2 (ordinary Petz map), to be compared with VWZ's lattice fit 0.070 c eta^2.

How to verify

rigor/quadratic_limit.tex Thm 4.2; tables in fidelity_tables.tex.

Evidence

• rigor/quadratic_limit.tex — document, at thm:lower
• numerics/make_tables.py — numerics

Related claims

None recorded.

Review

Review record: passed 2026-09-23 by REF-DEP-CFT-B3.

The referee's report and the card's event log stay in the private knowledge base; only the verdict, the date and the referee are published here.

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